What does the graph of (-2)^x look like?

  • Context: High School 
  • Thread starter Thread starter reaver
  • Start date Start date
  • Tags Tags
    Graph
Click For Summary

Discussion Overview

The discussion revolves around the graph of the function (-2)^x, exploring its behavior for different values of x, including integer and fractional values. Participants examine the implications of graphing this function in both the real and complex planes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in graphing (-2)^x and seeks assistance.
  • Another participant suggests calculating values for x and plotting them, but questions the meaning of "the graph."
  • A third participant notes that while integer values of x can be calculated, the function is generally undefined for non-integer values, leading to errors when using calculators for fractional x.
  • A question is raised about the possibility of graphing the function in the complex plane, challenging the notion of it being undefined for non-integral x values.
  • A later reply provides a method to express (-2)^x in terms of complex numbers, indicating that it results in a spiral in the complex plane, intersecting the real axis at integer values of x.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the function can be graphed for non-integer values of x, with some asserting it is undefined while others propose a complex representation.

Contextual Notes

The discussion highlights the limitations of calculators when dealing with non-integer exponents of negative bases and the dependence on definitions of functions in different mathematical contexts.

reaver
Can some one tell me what the graph of (-2)^x is i tryed but i only got errors.

Thank in advance for your help

reaver
 
Last edited by a moderator:
Mathematics news on Phys.org
what do you mean by "what is the graph"?

just take some values of x, work out y with a calculator and draw it on some graph paper!

or write a few program lines..
 
I wonder if Jonnylane tried doing that himself! If you try to graph y= (-2)x by plotting values, you can calculate values for integer values of x but that won't necessarily tell you the true graph. In this case it certainly doesn't!

If you try to use a calculator to calculate values for fractional x, you are going to get more error messages.

In general, the function ax is only defined for positive a. (-2)x is going to be undefined for almost all x!
 
Can the function be graphed in the complex plane, or is it truly undefined for nonintegral x values?
 
You can obtain values of (-2)^x for any x, but your calculator needs a little help because you obtain complex values:

(-2)^x
= (2ei[pi])x
= 2x (ei[pi])x
= 2x (cos([pi]x) + i sin([pi]x))

Which is a spiral in the complex plane, which touches the real axis for all integer values of x.
 

Similar threads

High School What Math Class Teaches us how to Draw a Graph?
  • · Replies 23 ·
Replies
23
Views
3K
High School Looking for free graphing calculator for two-variable inequality
  • · Replies 4 ·
Replies
4
Views
2K
High School Fractional/decimal powers
  • · Replies 10 ·
Replies
10
Views
3K
MHB Value of b, y-intercept of Quadratic graph
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Equation to graph a sine wave that acts like a point on a unit circle
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
3K
High School Graphing arccosine: What if we use different domains?
  • · Replies 7 ·
Replies
7
Views
2K
High School Correlation between shifting graph of a function and shifting the axes
  • · Replies 5 ·
Replies
5
Views
2K
High School Deriving the "third" kinematic equation using graphs
  • · Replies 21 ·
Replies
21
Views
1K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
3K